Story highlights

Bernie Sanders and Hillary Clinton are both trying to claim Barack Obama's legacy

Sanders is looking back to Obama's 2008 campaign and the hope and change message

Clinton is focusing on his time in the White House and governing

Adel, Iowa (CNN)Hillary Clinton and Bernie Sanders agree on one thing: They each believe they're the best positioned to carry on President Barack Obama's legacy.

Sanders is a movement candidate who has drawn massive crowds of young voters to his events, and frames himself as the successor to the man who as a candidate excited the Democratic Party like nobody else has this century. He is the 2008 Obama.

Clinton, an establishment candidate focused on governing, stresses her experience as Obama's secretary of state and touts her ability to navigate Washington and keep his accomplishments from being erased by Republicans. She is the White House-tested President Obama.

Their strategies reflect a nostalgic Democratic base that is split along demographic lines. Most Democrats give Obama high approval ratings, yet many still struggle to reconcile his soaring campaign rhetoric with what he has been able to accomplish -- or not accomplish -- as President.

"I think the American people, working people, young people, want to see real movement in this country, and I think we are tapping into that energy," Sanders said after meeting with Obama Wednesday for about in hour in the Oval Office.

Sanders: Candidate Obama

Wednesday's conversation came after Obama praised Clinton, and seemed to reject the notion that the Sanders campaign is an "analog" of Obama's 2008 effort.

But Sanders isn't waiting for Obama's endorsement. A recent Sanders ad features a rising sun on the horizon, reminiscent of Obama's 2008 logo. He has talked about change coming from the bottom up, echoing a favorite Obama phrase. His slogan—"A Future to Believe In"—is clearly borrowed from Obama's "Change We Can Believe In" motto.

In Iowa, Sanders has encouraged his supporters to see that same connection.

"It really reminds me very much of what happened here eight years ago. Remember that?" he said in Clinton, Iowa recently. "Eight years ago, Obama was being attacked for being pie in the sky, he did not have the experience. People of Iowa saw through those attacks then and they're going to see through those attacks again."

Clinton: President Obama

Clinton has wrapped herself in Obama's governing style, praising his approach to health care, gun control and college affordability and vowing to both protect and build on his accomplishments.

"It is time to pick a side," Clinton said in an ad she released on guns earlier this month. "Either we stand with the gun lobby or we join the president and stand up to them I am with him. Please join us."

And in defending her judgment on foreign policy, particularly on her vote to authorize the Iraq war, Clinton employs Obama as her validator.

"I think the American public has seen me exercising judgment in a lot of other ways," she said at CNN's Democratic Town Hall on Monday. "And, in fact, when that hard primary campaign was over and I went to work for President Obama and he ended up asking me to be secretary of state, it was because he trusted my judgment."

Polls show that Clinton has captured the most diverse portion of the Obama coalition. And her primary strategy also banks on winning part of the Democratic base, especially African-American voters, that she lost in 2008. That is key to states like South Carolina that the Clinton campaign is eyeing as a firewall against a possible Sanders sweep of Iowa and New Hampshire.

During a dinner in South Carolina earlier this month, Clinton said she "noticed that very often my name is linked to the President."

"Now I personally consider that a great compliment," Clinton added. In a Politico interview, Obama underscored a Clinton campaign theme.

"I think that what Hillary presents is a recognition that translating values into governance and delivering the goods is ultimately the job of politics, making a real life difference to people in their day-to-day lives," he said. "I don't want to exaggerate those differences, though, because Hillary is really idealistic and progressive."

For many in Iowa, Clinton's pitch that she is "Obama-plus" works.

"I love her idea of building on the progress (Obama made)," said Will Morrison, a 32-year old who attended Clinton's Tuesday townhall in Deborah. "I love Bernie, but I don't think his goals are realistic."

Highlighting differences with the President

Sanders, meanwhile, has attracted younger voters who are largely younger and whiter. For them, he represents a change to the status quo.

"Obama's done a lot of amazing things, but he has disappointed a lot of people," said Mykah Kennedy, 18, a student at Iowa Central Community College who was wearing a "Bernie is Magic" t-shirt. "When Clinton mentions Obama, it sounds like only 5% will get done rather than big change. With Bernie, it feels like a lot more will get done."

Sanders has both overtly and implicitly criticized Obama, suggesting that he left the movement he built on the campaign trail, rather than bringing it to the White House with him. Clinton has tried to exploit that fissure, mentioning in a recent debate in South Carolina that Sanders suggested a primary challenge to Obama before the 2012 election.

Speaking outside the White House Wednesday, Sanders highlighted his relationship with Obama, noting that they both campaigned for each other. But he also pointed to areas of disagreement.

"It is also no secret that we have, as is the case in a democratic society, we have differences of opinion," he said. "I was on the floor of the Senate for eight and half hours, in disagreement with him over taxes. We disagree over the (Trans-Pacific Partnership). But by and large over the last seven years, on major issue after major issue, I have stood by his side."

In turning to the campaign trail, Sanders has cited his Obama-like crowds — 15,000 in Minnesota on Tuesday --and said that he is connecting with young voters. Still, he downplayed expectations on turnout, suggesting he isn't quite like Obama.

"Obama in 2008 ran a campaign which is really going to stay in the history books. It was an unbelievable campaign," Sanders said this week during a press conference. "Do I think that in this campaign that we're going to match that? I would love to see us do that. I hope we do. But frankly I don't think we will. What happened in 2008 was extraordinary."